<p>I have the option of taking Linear Algebra or Calculus III next semester of my Freshman year in COLLEGE. University of Maryland. I'm pretty solid at math, coming from high school with a 5 on the calc 1 AP exam and a 4 on the calc 2 AP exam. (It was a year long course called calculus AB/BC, with AB as calc 1 and BC as calc 2. I don't know how it is for other schools). Regarding algebra, I believe I am good at that as well as doing derivatives and integrations requires you to be good at PEMDAS and general algebra, like substitution and all those specific rules.</p>
<p>So I am asking, which course will I be more SUCCESSFUL at? Linear Algebra, or Calculus III?</p>
<p>Calculus I && II were not that difficult for me, mostly because my teacher was outstanding. Series in calculus II was slightly challenging, and nothing more than that. And algebra is just plugging in numbers isn't it?</p>
<p>A semester-based Calculus III course will cover vectors, gradients, double/triple integrals and surface area problems (with Green’s Theorem).</p>
<p>Linear Algebra cover the theory and applications using matrices. Although the word “algebra” is in its title, linear algebra is far from “plugging and chugging”.</p>
<p>Two different topics.</p>
<p>It is hard to determine which course that you wii be more successful at because each person has different interests and passions.</p>
<p>Meaning you got a 4 on AP calculus BC with a 5 on the AB subscore?</p>
<p>If you want to take calculus 3, review the final exams for your college’s calculus 1 and 2 courses to make sure that you know all of the material in those courses. You may have to self-study small bits of material that were not covered in your AP course, or retake calculus 2 if your knowledge of the material leaves you struggling on those final exams.</p>
<p>Linear algebra really does not depend on calculus, even though it is usually taken after calculus 1 and 2. But if differential equations are combined into the course, then that does depend on calculus 1 and 2.</p>
<p>What is your likely major?</p>
<p>Most science majors that require one of these courses require both, but CS may require just linear algebra at some schools.</p>
<p>If it’s taught in a more “advanced” way, Calc III can depend on linear algebra (or at least LA will be useful to know). However, most courses with that title will probably assume little linear algebra background. It shouldn’t be too hard to figure which one this is. When I took Calc III I had not taken linear algebra and while I did fine, I can see the advantage of having some basic background in it. However, if you only have one option it might be a good idea to continue the calc sequence so you don’t forget stuff from I and II.</p>
<p>I have taught both. Much will depend on your interest, career path, and work ethic. I have seen many students assume linear algebra is easier and then get a D. We usually recommend linear alg. after Calc III. Does your school go to Calc IV or V? Everyone does not start differential equations in Calc III. You should have completed all forms of integration BEFORE lin alg. A physics background also helpful for calc.</p>
<p>You should know what derivatives (yes in multi dimensions) are before learning how they can be treated as linear operators between vector spaces.</p>
<p>I learned linear algebra before multivariable calculus and retrospectively I think that was a good choice.</p>
<p>
That’s kinda like saying, “You should know the fundamentals of aircraft construction before you take a physics class.” Yes, derivatives are an example of a linear operator, but that does not mean that linear algebra isn’t a legitimate subject in its own right.</p>
<p>My honest opinion would be the following: if you will be taking both classes anyway, take them in the order recommended by the university. If nothing else, it means that you’ll be taking the classes in the same order as most of your peers, which will make it easier for you to join a study group. If you only take one of the two classes, my recommendation would depend on what you want to do with that knowledge. For example, if you’re interested in computer science, you might benefit more from linear algebra. If you are interested in physics, you’d benefit more from multivariable calculus.</p>
<p>Maybe a decade or more ago, computer science majors were required to take as much math as the engineering majors. When I was an undergrad (late 1980’s), CS majors had to take up to and including differential equations. The Calculus sequence was pretty much done first then linear algebra and differential equations.</p>
<p>Nowadays, most CS programs only required Calculus I, Calculus II, then Linear Algebra…hence why some folks will differ in opinion on when to take linear algebra.</p>